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Existence of stable standing waves and instability of standing waves to a class of quasilinear Schrödinger equations with potential
For a class of quasilinear Schrödinger equations with harmonic potential of the formwe prove firstly the existence of stable standing waves for 1 < p < 3 + 4N and then study the instability of standing waves for 3 + 4 N ≤ p < 3N+2 N-2 .Our results indicate …